The radionuclide ^ { 22 } Na is a potential astronomical observable that is expected to be produced in classical novae in quantities that depend on the thermonuclear rate of the ^ { 22 } Na ( p, \gamma ) ^ { 23 } Mg reaction . We have measured the strengths of low-energy ^ { 22 } Na ( p, \gamma ) ^ { 23 } Mg resonances directly and absolutely using a radioactive ^ { 22 } Na target . We find the strengths of resonances at E _ { \textrm { p } } = 213 , 288 , 454 , and 610 keV to be higher than previous measurements by factors of 2.4 to 3.2 , and we exclude important contributions to the rate from proposed resonances at E _ { \textrm { p } } = 198 , 209 , and 232 keV . The ^ { 22 } Na abundances expected in the ejecta of classical novae are reduced by a factor of \approx 2 .